The new 'Help to Save' accounts being announced in this week's budget were "on the surface a really good idea", director Niall Cooper said.
On Premier's News Hour he warned that many people would not be able to save £50 a month - the amount needed to be offered a bonus of up to £1,200.
Prime Minister David Cameron has announced the scheme will be open to millions of employees who receive in-work benefits, such as tax credits, within two years.
Under Help to Save, around 3.5 million workers on universal credit or working tax credits will be able to save up to £50 a month and receive a bonus of 50% - a maximum of £600 - after two years. Savers can continue to use the scheme for a further two years and earn up to another £600.
Niall Cooper said: "I think the challenge is actually that so many people now are struggling to make ends meet on a week to week basis that how many people will actually be able to take up the scheme.
"Many people in this situation are already in debt. People, I'm sure, would love to be able to put aside £50 a week but if you can't make the money even stretch to the end of the week I think this will be beyond most people."
Chancellor George Osborne said: "This Government is determined to improve the life chances of the poorest in our society and our new Help to Save scheme will mean millions of low income savers across the country could now receive a Government bonus of up to £1,200 to help them build up their savings."
Shadow work and pensions secretary Owen Smith dismissed the savings scheme, claiming that benefits cuts will mean families struggling to make ends meet rather than having money to put aside.
He said: "This is like stealing someone's car and offering them a lift to the bus stop."
